Minimax design of two-channel low-delay perfect-reconstruction FIR filter banks

Abstract

The authors deal with the design problem of low-delay perfect-reconstruction filter banks for which the FIR analysis and synthesis filters have equiripple magnitude response. Based on the minimax error criterion, the design problem is formulated in such a manner that the coefficients for the FIR analysis filters can be found by minimising the weighted peak error of the designed analysis filters, subject to the perfectreconstruction constraints. A design technique based on a modified dual-affine scaling variant of Karmarkar's algorithm, in conjunction with approximation schemes, is then developed for solving the resulting nonlinear optimisation problem. The effectiveness of the proposed design technique is demonstrated by several simulation examples. 2 Low-delay perfect-reconstruction FIR filter banks 15

An efficient method for designing two-channel PR FIR filter banks with low system delay

“…2] (30 dB versus 25 dB). It is also noted that the design and implementation complexities of the proposed method are very low and there is no reconstruction error, which is always present in other methods based on constrained nonlinear optimization [3], [7]. Furthermore, as mentioned earlier, the proposed filter bank structure is still PR, even under coefficient quantization, unlike the direct form in [4].…”

“…The design complexity of the proposed method is also much lower than the unconstrained nonlinear optimization methods in [5] and [6], thanks to the Remez Exchange algorithm. The overall performance comparison between the proposed method and the conventional low delay filter bank design methods [3]- [5] and [7] are summarized in Table I, where the arithmetic complexity is simply defined as the number of multiplications and additions per sample in implementing the filter bank. This demonstrates the good performance, flexibility, low implementation, and design complexities of the proposed method as compared with conventional methods.…”

“…Conventional methods for designing low delay two-channel PR FB are usually based on numerical optimization [3], [7], which produces FB that is only pseudo-PR. More recently, several factorizations for PR low delay FB were reported [5], [6].…”

Design and multiplier-less implementation of a class of two-channel PR FIR filterbanks and wavelets with low system delay

“…2] (30 dB versus 25 dB). It should be noted that due to the simplified structure of the proposed filterbank, its design complexity is very low, and there is no reconstruction error, which is always present in other methods based on constrained nonlinear optimization [10], [20].…”

“…One problem with the optimization approach is that the filterbanks so obtained are in general not PR (pseudo PR). This is also a major problem of other related works based on optimization techniques [11], [13], [15], [18]- [20]. One solution to this problem is to employ filterbanks that are inherently or structurally PR.…”